Paternity blood tests are very specialized tests not done at most labs. If you do an internet search for 'paternity testing,' you will find several labs throughout the US that can test samples for you, but you need to contact them for the paperwork and a 'kit'. Some labs will also help you locate a clinic nearby to help you with getting the specimens.
Some labs are independent: that is, they'll send you the paperwork and the kit, but you have to find the provider to obtain the specimen. If you are looking to do this prenatally, you may need to find a private doctor who does amniocentesis or a larger clinic/hopital for the amnio or chorionic villus sampling. When you contact paternity labs directly, most of them are pretty helpful and forthcoming with information.